High speed surface finishing method



May 26, 1970 MASAHISA MATSUNAGA ET 3,513,604

HIGH SPEED SURFACE FINISHING METHOD 7 Filed Nov. 22, 1967 5 Sheets-Sheet 1 INVENTORS HISAMINE KOBAYASHI ATTORNEYS MASAHISA MATSUNAGA May 26, 1970 MASAHISA MATSUNAGA ET 3,513,604

I HIGH SPEED SURFACE FINISHING METHOD Filed Nov. 22, 1967 3 Sheets-Sheet 2 ZOO /MlNf" FIGJO INVENTORS MASAl-HSA MATSUNAGA HISAMINE KOBAYASHI ATTORNEYS May 26, 1970 MASAHISA MATSU NAGA ET AL HIGH SPEED SURFACE FINISHING METHOD Filed Nov. 22, 1967 5 Sheets-Sheet 3 MASAHISA MATSUNAGA H ISAMINE KOBAYA SH! ATTORNEYS United States Patent 3,513,604 HIGH SPEED SURFACE FINISHING METHOD Masahisa Matsunaga, Tokyo, and Hisamine Kobayashi,

Nagoya, Japan, assignors to Kabushiki Kaisha Shikishima Tipton, Nagoya, Japan Filed Nov. 22, 1967, Ser. No. 685,028 Claims priority, application Japan, Nov. 26, 1966, 41/77,653 Int. Cl. B24b 1/00 US. Cl. 51--313 5 Claims ABSTRACT OF THE DISCLOSURE Within a barrel having an internal cross section in the shape of an equilateral polygon having from five to eight sides there is loaded a mixture of workpieces and abrasives in an amount equal to approximately a half of the internal volume of the barrel. The barrel is rotated in one direction about its own axis with the number n of rotation in a unit time and simultaneously revolved in the opposite direction about a fixed axis parallel to and positioned a distance R from the axis of the barrel with the number N of revolution in the same unit time where R is greater than a radius r of a circle inscribed in the polygon. Using a Cartesian orthogonal coordinate system (R/r, n/N)? and 1 z0.3-1 and 1.53

This invention relates to improvements in a method of surface finishing workpieces within a barrel of an equilateral polygonal cross section gyrating at a high speed. In the past, there have been proposed various types of the surface finishing methodsreferredto. For example, US. Pat. No. 3,233,372 to H. Kobayashi disclosesa surface finishing method comprising loading a mixture of workpieces and granular abrasives into at least one barrel having an internal cross section in the shape of an equilateral polygon having from five to eight sides in such a manner that the mixture fills about one half of the barrel, and causing the barrel to gyrate about a fixed axis parallel to the axis of the barrel but not passing through the interior of the barrel while maintaining the barrel in a fixed orientation, at such a speed that thecentrifugal force on the mixture in the barrel is greater than the force of gravity thereon so that relative movement occurs between the mixture and the abrasives in a free surface layer only of the mixture in the barrel and successive portions of the mixture are brought into and removed from the surface layer by the gyration of the barrel.

According to the surface finishing method just outlined the barrel may revolve about the said fixed axis in one direction while at the same time it rotates about its own axis in the opposite direction so as to maintain the barrel in the fixed orientation. Thus it will be appreciated that the barrel gyrates with a ratio of the number n of rotation to the number N of revolution in a unit time of the barrel remaining unchanged or equal to minus one. The term minus means that the rotation is effected in the direction opposite to the direction of revolution. While this ratio having a minus one value generally gives the satisfactory results it has been found that, if the ratio is higher or less than minus one, the operation may become greatly dangerous unless a ratio of a radius R of revolution (or a distance between the said fixed axis and the axis of the barrel) to a radius r of a circle inscribed in the polygonal cross section of the barrel will be properly selected.

Also U.S. Pat. No. 2,937,814 to A. Ioisel discloses a ball crusher comprising a plurality of circularly cylindrical tubs gyrating at a high speed and teaches the preferred relationship between a distance from the axis of the crusher tub to the axis of the associated rotating frame and the inside radius of the tub and between a speed of revolution of the tub in relation to the frame and a speed of rotation of the frame. The latter patent is based on the phenomena that a mass comprising a mixture of workpieces to be crushed and crushing balls falls downwardly along the internal wall of the tub while it maintains a segmentally cylindrical shape substantially similar to its shape in which the mass has been initially loaded in the tub or while the mass in the segmentally cylindrical shape collapses to a great extent to rush down along the internal *wall of the tub thereby to crush the workpieces against the internal tub wall. Thus such a crusher relies upon the utilization of the centrifugal force exerting on the outermost portion of the mass sliding down along the internal wall of the rotating and revolving tub. This is distinctively different from the first cited patent and the present invention in which the centrifugal force is exerted only on a free surface layer of a mass having successively dilferent mass portions 'brought into and removed from it.

Accordingly it is an object of the invention to determine various design parameters suitable for safely and efficiently carrying out a surface finishing method utilizing the centrifugal force on a free surface layer of a mass or workpieces with or without abrasives having the successively different portions thereof brought into and removed from the layer within a barrel effecting rotational and revolutional movements in the opposite directions.

Briefly, the invention accomplishes this object by the provision of a surface finishing method comprising loading a mixture of workpieces and abrasives into at least one barrel having an internal cross section in the shape of an equilateral polygon having from five to eight sides in such a manner that a substantial free space is left in the barrel, and causing the barrel to rotate in one direction about its own axis with the number n of rotation in a unit time while at the same time the disc unit causing the barrel to gyrate in the opposite direction about a fixed axis parallel to and located at a distance R from the axis of the barrel with the number N of revolution in the same unit time where R is greater than a radius r of a circle inscribed in the equilateral polygon, the method being characterized in that, referring to a Cartesian orthogonal coordinate system (R/r, n/N), the method is carried out at an operating point (r, N) whose coordinates E It T N meet the relationships -1 -0 3 -1 and 1 5 s N r r- The abrasives may be conveniently selected from the groups consisting of organic, inorganic and metallic materials and in the form of a liquid, a solid or mixtures thereof.

The mixture of workpieces and abrasives may be advantageously loaded in an amount equal to from 40 to 70% and preferably from 50 to 60% of the internal volume of the barrel.

The barrel may gyrate at a speed of /2R r.p.m. or more in accordance with the specific gravity and fluidity of the mixture therein, where R is expressed in meters.

The invention will become more apparent from the following detailed description taken in conjunction with the accompanying drawings in which:

FIG. 1 is a front elevational view of an apparatus embodying the principles of the invention;

'FIG. 2 is a side elevational view of the apparatus as viewed on the righthand side of FIG. 1;

FIG. 3 is a fragmental side elevational view, partly in section of a drive for rotating and revolving a barrel in the opposite directions;

FIG. 4 is a sectional view of barrels of different radial dimensions capable of being selectively mounted in a barrel housing shown in FIGS. 1 and 2 with a distance R between the axes of revolution and rotation of the barrel remaining unchanged, the section being taken along the line IVIV of FIG. 2;

FIG. 5 is a view similar to FIG. 4 but illustrating barrels of common radial dimension selectively disposed at different distances from the axis of revolution thereof;

FIG. 6 is a view similar to FIG. 4 but illustrating the case R/r has different values while R+r' remains unchanged;

FIG. 7 is a diagram useful in calculating a movement speed of an arbitrary point on a barrel;

FIG. 8 is a diagram uesful in obtaining an equation for a locus described by the point A shown in FIG. 7;

FIG. 9 is a graph plotting a centrifugal force on each of three preselected portions of the barrel against a ratio between the numbers n. and N of rotation and revolution in a unit time of the barrel;

FIG. 10 is a graph illustrating the experimental relationship between the total amount of workpieces removed in polishing and the number of revolution in a unit time of the barrel with R, r constant and n/N=1 where r is a radius of a circle inscribed in the internal cross section of the barrel;

FIG. 11 is a graph illustrating the relationship between a polishing efiiciency and n/N with R and r constant;

FIG. 12 is a graph plotting the centrifugal force and the polishing efiiciency against R for n/N=-1;

FIG. 13 is a graph plotting the polishing efiiciency against n/N for different values of R/r;

FIG. 14 is a graph illustrating the values of n/N with which the polishing efiiciency is maximum for different values of R/r;

FIG. 15 is a graph illustrating the dependency of the polishing efficiency upon both n/N and R/r with r and N remaining unchanged;

FIG. 16 is a graph plotting the polishing efliciency against n/N for different values of R/r with R+r remaining unchanged;

FIG. 17 is a graph illustrating a curve for the maximum polishing efficiency and a curve for polishing efficiency with n/N=1 against R/r; and

FIG. 18 is a graph illustrating the efficient ranges of n/N and R/r taught by the principles of the invention.

The invention based upon the discovery that, upon surface finishing workpieces within a gyrating barrel with abrasives in such a manner that the polishing action is accomplished only on a free surface layer of a mixture of workpieces and abrasives in the barrel and that successive portions of the mixture are brought into and removed from the surface layer by the gyration of the barrel, a safe, efiicient finishing operation is performed by properly selecting the radii of revolution and rotation of the barrel, and the numbers n and N of rotation and revolution in a unit time of the barrel for a negative value of n/N the absolute value of which is greater than unity.

Also it has been found that the barrel should have an internal cross section in the shape of an equilateral poly- 'gon having from five to eight sides. If a barrel is in the shape of an equilateral triangle or square its diagonal is excessively greater than the said minimum distance.

With a gyrating barrel of such a shape having loaded therein about 50% by volume of a mass the centrifugal force due to the gyration of the barrel causes the surface layer of the mass positioned on a surface passing through a diagonal to be transferred on the succeeding surface passing through the next one of the said minimum distance in such a manner that the central portion of the surface layer is raised in the shape resembling a curling wave which, in turn, strikes against the opposite side of the barrel with the result that the satisfactory surface finishing operation is not performed.

With a barrel having an internal cross section in the shape of an equilateral polygon having from five to eight sides, the surface mass layer is smoothly transferred from one surface to the next without any curling wave occurring. On the other hand, a barrel having an internal cross section in the shape of an equilateral polygon having nine or more sides resembles a barrel of circular cross section in operation. A mass in such a barrel slides along the internal wall thereof resulting in uneven finishing.

It has further been found that the barrel should, as a rule, gyrate at a minimum speed corresponding to 80/x/2R r.p.m. where R is a radius of revolution of the barrel in meters. It will be understood that the higher the speed the higher the polishing efficiency .will be. However, in view of the standpoint of the mechanical strength of presently available materials for the apparatus, a maximum speed of gyration will be 350/ /2R.

A proportion of workpieces to abrasives may preferably range from 1:0 to 1:10. A mixture of workpieces and abrasives having the proportion just specified is loaded in a barrel such as above described in an amount equal to from to 70% and preferably to from to on the basis of the internal value of the barrel.

Abrasives used with the invention may be organic, inorganic or metallic materials in the form of a liquid, a powder, a spherical solid, a shaped solid or mixtures thereof.

Further the invention is equally applicable to either of the wet and dry processes.

Referring now to the drawings and more particularly to FIGS. 1 and 2, there is illustrated a surface finishing apparatus constructed in accordance with the principles of the invention. The arrangement illustrated comprises a frame work 10 constructed by members of L-shaped section, a main horizontal shaft 12 journalled at both ends by a pair of bearings 14, 14 disposed on the top of the frame work 10, and a pair of spaced support discs 16, 16 secured adjacent one end portion of the main shaft 12 and having sandwiched therebetween a plurality of sleeves 18 disposed at substantially equal angular intervals on the outer peripheral portion. A cylindrical housing 20 is carried in cantilever fashion by a barrel shaft 22 supported in each sleeve 18 and has selectively mounted therein a plurality of barrels 24a, b and 0 different in radial dimension (see FIG. 4). While the barrel 24 is shown as having a hexagonal cross section it is to be understood that it may be of a regular pentagon, septangle, or octangle as previously pointed out.

Each barrel shaft 22 is provided at that end remote from the associated housing 20 with a sprocket wheel 26 operatively coupled to a different one of a plurality of aligned sprocket wheels 28 mounted on the main shaft 12 for rotation relative to the latter through an endless chain 30, the wheels 28 being integral with each other.

An electric motor 32 is rigidly secured on the bottom portion of the framework '10 and has a pulley 34 secured on its output shaft (not shown). The pulley 34 is operatively coupled to another pulley 36 mounted on the main shaft 12 at one end through an endless belt 38. Another electric motor 40 suitably fixed on the framework 10 has a pulley 42 mounted on its shaft to be operatively coupled to a speed change gearing 44 through an endless belt 46 and an input pulley 48 to the gearing.

The latter includes an output pulley 50 operatively coupled to a preselected one of the sprocket wheels 28 through an endless belt 52. With the arrangement illustrated the motor 32 is rotated in the direction of the solid arrow 54 to drive the support discs 16 in the direction of the solid arrow 55 while the motor 40 may be rotated the direction of the solid arrow 56 or 57 to drive the sprocket wheels 28 and therefore the housings and barrels 20 and 24 in the direction of the solid arrow 58 or 59 (see FIG. 3).

From the foregoing it will be appreciated that when the discs 16, 16 are rotated at a uniform speed in the direction of the solid arrow 55 about the axis of the main shaft 12. and simultaneously the barrels 24 are rotated at a uniform speed in the direction of the solid arrow 58 or in the direction opposite to the direction to rotate the supports about the axes of the respective shafts 22. Thus such motion of the support discs and barrels will resemble gyration of the barrels fixed to the discs.

As previously described the support discs 16 can be,

as a rule, revolved at a high speedequal to or greater solid arrows 55 and 58 in FIG. 3, the ratio n/N may be considered to have the plus sign While if they are driven in the opposite directions as shown at the arrows 55 and 59 the ratio n/N will have the minus sign. With the ratio n/N positive, the mass within the barrel will flow in the direction of the arrow 60 shown in FIG. 3. On the other hand, a negative value of the ration/N will cause the mass to slide in the dotted arrow 61 shown in FIG. 3.

It will'be readily understood that the larger the value R the higher the centrifugal force and hence a polishing efliciency will be.

The motion of thesupport discs and barrels 16and 24 as above outlined will now be theoretically described in conjunction with FIG. 7. In FIG. 7, itis assumed that a support disc such as .shown in FIGS- 1 and 2 is rotated about its center .of rotation represented by the origin of a Cartesian orthogonal coordinate system (x, y) while at the same time a barrel such as shown in FIGS. 1 and 2 is rotated about its center 0 of rotation lying on a fixed circle whose center is at the origin 0. Since the barrel has an internal cross section in the shape of an equilateral polygon it is represented by a circle inscribed in the polygon in FIG. 7 and'the following figures. It is further assumed that for any given time the center 0' of the barrel, assumes an angular position on with respect to the x axis and that a preselected point A on the barrel circle has an angular position with respect to the x axis at the same time.

.Then the point A has a linear velocity V due to revolution of the disc and a linear velocity V due to rotation of the barrel expressed by the following equations.

V =21rRN V 21rrn where R isa radius of rotation of the disc or the radius of the fixed circle, 1 a distance of the point A from the center 0' of the barrel or the radius of the circle 0' and N and n are the numbers of rotation of the disc and barrel in a unit time. The two vectors V and V are vectorially summedup to provide a movement velocity V of the point A. Namely it is expressed by the equation where x and y represent the coordinates of the point In FIG. 8 similar to FIG. 7 is useful in obtaining an equation for a locus depicted by the point A during the movement as above-described. When the radius vector 00' has been rotated about the origin 0 through an angle e and is located in its position 00'' the radius vector OA' is rotated through an angle fl-l-e with respect to the x axis and further through angle during rotation of vector 00 through the angle 13 until it reaches its position 0"A. Therefore the equation for a locus depicted by the point A is expressed by the equations (3) x=R cos +;3)+r cos [5+ 7%)] Since a radius p of curvatures at any point on a curve y=F(x) is defined by the equation dy 2 3 l 15 P- y a radius p of curvature at any point on the locus expressed by the Equations 3 is given by the equation In terms of the acceleration g due to the gravitation an acceleration due to the centrifugal force on the point A can be expressed by V /pg. The Equations 2 and 5 are substituted in V g resulting in where x +y (Rir) two points are farthest from and nearest to the origin 0 respectively and designated by the reference Roman numerals I and III and where x +y =R -|-r a point lies on each of intersections of the circle 0' and a diameter perpendicular to the diameter passing through the points I and III and designated by the reference Roman numeral II as shown in FIG. 9.

The centrifugal forces on those points I, H and III are expressed respectively by the equations The centrifugal force on the point II is nearly equal to that on the center of the barrel.

Assuming that N=180 r.p.m., R=30 cm. and r= cm., the values of the centrifugal forces on the points I, II and III are illustrated in FIG. 9 wherein the abscissa represents n/N and the ordinate represents V g. Curves I, II and III are plotted for the points I, II and III respectively. A useful range of n/N can be determined from curves I, II and III as will be subsequently described.

For a centrifugal force whose value is negative at the innermost point III, a mass in a barrel begins to stick on the entire internal wall of the barrels. Therefore the centrifugal force on that point must be positive.

In other words, the value of n/N should hold the following relationship For example, for R/r=3, n/N must meet the following in equality This means that the useful range of n/N is extremely narrow.

To calculate a polishing efficiency, experiments were conducted with only N variable under the following conditions:

Machine used: High speed gyration barrel finishing machine sold by the applicant.

Barrel type: Hexagonal shape horizontally disposed.

Barrel size: 164 mm. in inside minimum dimension and 275 mm. in length.

Radius of revolution R: 268 mm.

Abrasives: Standard chips sold by the applicant and including essentially of 68% of alumina and 32% of a bonding material or silica by weight formed in spheres whose diameter is of 6:0.5 mm.

Charge: 50% of internal volume of barrel.

Water: 1 litre.

Compound: 10 g. of (10-200 (trademark) including Na.;P O 30% NaNO Time: One hour.

The results of experiments are illustrated in FIG. 10 wherein the abscissa represents an amount W of metal removed in grams in polishing and the ordinate represents the number of revolutions per minute. Curve illustrated in FIG. 10 can be expressed by the equation where K" is a constant.

Assuming that the amount of workpieces removed in polishing is proportional to a sliding cycle n/N per one complete rotation of the disc, of the mass, the number of rotation of the latter and a Sth power of a value of the centrifugal force F exerted on the central portion of the mass the relationship between the centrifugal force and the amount Q of workpieces removed is expressed by the equation (9) W=K"NF and F is expressed by 2 2 n 3 1 N R F) g r oerr Therefore the polishing efiiciency is expressed by the equation where s has a value of 1.24. In FIG. 11 wherein the abscissa represents the n/N and the ordinate represents the relative polishing efliciency, an upper curve labelled 160 r.p.m. was plotted for N =160 r.p.m. and a lower curve labelled r.p.m. was plotted for N =120 r.p.m. calculated from the Equation 10, assuming that the relative polishing efiiciency equals unity when n/N=l and N r.p.m. Also the symbols dot in circle and white circle" designate the measured values of the relative polishing efficiency. For the upper curve illustrated in FIG. 11, the relationship between n/N and the measured amount of workpieces removed in polishing is listed in the following Table I.

TABLE I Relationship between n/N and measured amount of workpieces removed with N =160 r.p.m.

From FIG. 11 it will be seen that the theoretical values of the relative polishing efliciency are well identical to the corresponding measured values thereof within a range of n/N between 0 and -2. This means that the Equation 10 can be effectively used to calculate a polishing efiiciency of any gyration barrel finishing within the range of n/N just specified.

On the other hand, FIG. 11 shows that for any positive value of n/N the theoretical values of the relative polishing efliciency are very dilferent from the corresponding measured values thereof. For example, its measured value is a fraction of its corresponding theoretical value for n/N=+0.5. This offers a proof that for n/N=+0.5 the centrifugal force on the point III as shown in FIG. 9 tends to approximate zero value whereby a mass in a barrel has been already difiicult to effect the normal sliding motion and is in its floating state immediately before it sticks on the internal barrel wall.

As shown in FIG. 11, any negative value of n/N having an absolute value exceeding 2 (two) causes the polishing efficiency to decrease but it greatly increases the centrifugal force on the point I as will .be seen in FIG. 9. For this reason, any negative value of n/N having an absolute value exceeding two is unsuitable for use in this case, that is R/r=3.

Thus it has been found that upon practicing the invention, a value of n/ N be negative rather than positive.

To determine the dependency of the polishing efliciency upon R/ r experiments were conducted with an apparatus such as shown in FIGS. 1 and 2 wherein R is variable, r=0.25 cm., N=240 r.p.m. and n/N=l. Their results are illustrated in FIG. 12 wherein the axis of abscissae represents R in cm. while the righthand axis of ordinates represents the polishing efficiency Q relative to that at R/r=3 and N='160 r.p.m. and the left hand axis of ordinate represents a ratio an acceleration cc of the point II see FIG. 9) to the acceleration g due to the gravitation. Solid curve designates the efficiency and dotted curve designates the acceleration; As previously described, the larger the R the higher the'polishing eflic'iency will be. The data in FIG. 12 clearly show this. If delicate and/or brittle workpieces are applied with the centrifugal force excessively high, then they are apt to be deformed and/ or damaged. Therefore, the present invention is beneficial in that upon surface finishing delicate and/or brittle workpieces, a value of the centrifugal force'suitable for them can "be preliminarily determined.

j The polishing efficiency' will now be described with respect to the case'R/r is variable while R remains unchanged and the case both n/N and R/r are variable in order to select the values of R and r' from the standpoint of design. A change in polishing efficiency dependent upon R/ r can be calculated from the Equation 9 and is illustrated in FIG. 13 wherein the abscissa represents n/N and the ordinate represents the polishing efficiency Q relative to that at n/N =1 and R/r=3 and with a parameter being R/ r, assuming that R is constant. FIG. 13 corresponds to FIG. 4 wherein a plurality of barrels such as hexagonal barrels 24a, bjand. c having different radial dimensions of r r;,, and r;., are selectively mounted in coaxial relationship in the housing 20. FIG. 13 shows that the larger the R/ r the higher the polishing efliciency. This is because the workpieces contained in one barrel are relatively low in number. a

As shown in FIG. 5, a barrel 24 may be rotatably mounted on the support discs 16 at different distances R R and R from the center 0 of rotation of the disc to vary R/r. The relative polishing efiiciency of such an arrangement is calculated from the Equation by varying R and n while r and N remains unchanged and illustrated in FIG. wherein the abscissae and ordinates have the same meaning as in FIG. 13. From FIG. 13 it will be seen that a maximum value of the polishing efficiency and a range within which polishing can be satisfactorily accomplished depends upon R/r.

FIG. 14 shows a curve for the relationship between n/N and R/r which gives the maximum polishing efiiciency referred to a Cartesian orthogonal coordinate system (R/r, n/N). Curve shown in FIG. 14 can be expressed by the equation Since a range of n/N within which the polishing efiiciency decreases with an increase in absolute value of n/N will increase the centrifugal force on the outermost point on the associated barrel as will be understood from the description for FIG. 11, the invention contemplates to use value of n/N above the straight line shown in FIG. 14. In other words, the Equation 11 gives one-limit of n/N.

Further R/ r may be changed while R-+r remains unchanged. For example, as shown in FIG. 6, a plurality of barrels such as hexagonal barrels 24, 24 and 24" having different radial dimensions r r and r may be selectively disposed at different distances R R and R such that R+r R +r and R +r are equal to each other. In this case the polishing efliciency is given by the equation enter a wherein K is a constant and s has been previously described. FIG. 16 wherein the abscissa and ordinate have the same meaning as in FIG. 13 illustrates curves for the Equation 12 for various R/r. A negative figure having a leader line from adjacent a maximum point on each curve is the particular value of n/N providing the corresponding maximum value of the polishing efficiency. From FIG. 16 it will be seen that the smaller the R/r the higher the polishing efficiency. However it has been found that the polishing efiiciency increases to a certain limit as R/r decreases and that it has a maximum value adjacent r/ (R+r)=0.6 or R/ r=2/ 3 after which the polishing efficiency decreases. The data in FIG. 17 shows this. In FIG. 17 the abscissa represent r/c, where c=R+r and the ordinate represents the relative polishing efficiency Q. Also there is shown a curve for the relative polishing efficiency for n/N=1 or of the above cited US. Pat. No. 3,233,372.

Thus the ratio R/r can now be selected from a domain defined by the upper and lower curve portions shown in FIG. 17. 1

From the foregoing it has been concluded that any negative value of n/N in excess of that providing a maximum value of the polishing efficiency as above described has no beneficial effect on the polishing .process but it merely increases the centrifugal force on the outermost position such as the point I of the barrel and accordingly a danger of the operation. Also, as seen in FIG. 11, any value of n/N between minus unity and zero decreases a .distance through which a mass can slide down in the associated barrel. This is disadvantageous; in that the polishing efiiciency decreases and nevertheless the centrifugal force on the outermost portion of the barrel increases. Further any positive value of n/N is not at all advantageous as shown in FIG. 11.

More specifically, if an absolute value of minus n/N increases beyond unity for any given value of R/r, then a mass in a barrel increases in a distance of its sliding movement and thereby the polishing efficiency increases. The above-mentioned maximum value of the polishing elficiency monotonously increases before the ratio n/N reaches a certain value (see FIG. 11). However the centrifugal force on the surface layer of the mass in the barrel decreases as shown at curve II in FIG. 9. This means that a large negative value of n/N is possible to surface finish workpieces into relative flat surfaces and is especially suitable for precise or glossy polishing.

Also it will be understood that the more the value of n/N approximates minus unity the shorter the distance through which a mass slides in the associated barrel will be and therefore the higher the centrifugal force on the sliding mass will be. Therefore it is apparent that any negative value of n/N greater than and approximating minus unity is suitable for heavy grinding.

From the foregoing it has finally been concluded that the surface finishing method according to the principles of the invention must be performed at an operating point positioned in a hatched domain shown in FIG. 18. Referring to a Cartesian orthogonal coordinate system (R/ r, n/N), the hatched domain is defined by a straight line expressed by and a straight line expressed by represents the maximum values of the polishing efficiency. Also in FIG. 17, a hatched portion between the two curve portions designate an operating domain and its preferred domain for R/r and n/N with R-I-r remaining unchanged. Similarly the hatched portion defined by 1 1 R/r=1.5 and R/r=8 and the preferred'portion is defined by R/r=2 and R/r=5.

In order to change R/ r, the arrangement shown in any of FIGS. 4, 5 and 6 may be used. The speed change gearing 44 is used to change n/N. Alternatively the motor 32 may be a variable speed motor. If desired, the main shaft 12 may change in speed of rotation to change n/N.

The results of tests indicated that the present method had the polishing efficiency equal to from 60 to 1000 times that of conventional rotating barrel finishing methods and to from 15 to 300 times that of the conventional vibrating barrel finishing methods.

It is to be noted that upon selecting the values of MN and R/ r, the material, shape and dimension of workpieces, the type of abrasives, etc. should be considered.

What we claim is:

1. A surface finishing method comprising loading a mixture of workpieces and abrasives into at least one barrel having an internal cross section in the shape of an equilateral polygon having from five to eight sides and in such a manner that a substantial free space is left in the barrel, and causing the barrel to rotate in one direction about its own axis with the number n of rotation in a unit time while at the same time causing the barrel to gyrate in the opposite direction about a fixed axis parallel to and located at a distance R from the axis of the barrel where R is greater than r with the number N of revolution in the same unit time where R is greater than a radius r of a circle inscribed in the equilateral polygon, the method being characterized in that, referring to a Cartesian orthogonal coordinate system (R/r, n/N), the method is carried 12 out at an operating point whose coordinates meet the relationship that n/N has a value negatively less than -1 but not negatively less than -0.3(R/r)1, and R/r has a value of from 1.5 to 8.

2. A surface finishing method as claimed in claim 1, characterized in that the abrasives are one selected from the group consisting of organic, inorganic and metallic material and mixtures thereof and from the group of consisting of a liquid, solid and mixtures thereof.

3. A surface finishing method as claimed in claimi1, characterized in that the mixture of workpieces and abrasives is loaded in the barrel in an amount equal to from to on the basis of the internal volume of the barrel.

4. A surface finishing method as claimed in claim 1, characterized in that a proportion of the workpieces to the abrasives ranges from 1:0 to 1:10.

5. A surface finishing method as claimed in claim- 1, characterized in that the barrel gyrates at a speed of at least /2R r.p.m. where R is the radius of revolution in meters of the barrel.

References Cited UNITED STATES PATENTS 3,233,372 2/1966 Kobayashi 51-313 LESTER M. SWINGLE, Primary Examiner U.S. Cl. X.R. 

